The invention relates generally to communications and particularly to a method and apparatus for near optimal joint channel estimation and data detection to improve channel tracking and, thus, improve link robustness.
The rapid growth in the use of the Internet and the increasing interest in portable computing devices have triggered the desire for high-speed wireless data services. One of the more promising candidates for achieving high data rate transmission in a mobile environment is Orthogonal Frequency Division Multiplexing (OFDM), which divides the wide signal bandwidth into many narrow-band subchannels, which are transmitted in parallel. Each subchannel is typically chosen narrow enough to eliminate the effects of delay spread. Coded OFDM (COFDM) systems, which combine both OFDM and channel coding techniques, are able to improve the performance further by taking advantage of frequency diversity of the channel.
Though both differential and coherent demodulation can be applied in a COFDM system, the latter leads to a performance gain of 3 to 4-dB in signal-to-noise ratio (SNR) with accurate channel estimation. Channel estimation techniques realized by a frequency-domain filter using Fast Fourier Transform (FFT), followed by time-domain filters for a COFDM system with Reed-Solomon (RS) coding have been proposed. These channel estimation techniques, while good, did not provide the near optimal channel estimation required for data-decoding with improved channel tracking capability for reliable link performance even under high user mobility and/or high RF carrier frequency.
The physical layer configuration is shown in FIG. 1A. At the transmitter, the encoded data stream is sent to an OFDM transmission branch. The data stream may, for example, be convolutionally encoded. The encoded data stream may then be optionally interleaved. If the encoded data stream is interleaved in the transmitter then the receiver must correspondingly deinterleave the data stream. After interleaving, the transmitter modulates the encoded data stream. By way of example, QPSK modulation is used. The signal is then subjected to inverse Fast Fourier Transformation and transmitted, in the present invention over the air.
Correspondingly, a receiver accepts multicarrier transmitted signals and subjects these received signals to Fast Fourier Transformation. The transformed signals are concurrently fed into a channel estimator and demodulators. The demodulated signals are combined in a maximum ratio combiner, optionally deinterleaved and decoded.
An OFDM signal is divided into a number of subchannels. By way of example, an OFDM signal bandwidth is divided into 120 6.25-kHz subchannels with QPSK modulation on each subchannel. At the receiver, the demodulated signals from two receiving branches are combined using maximal ratio combining and then decoded. With a symbol period of 200 xcexcs (including a 40-xcexcs guard interval) and xc2xd-rate coding, a maximum information rate of 600 kbps can be achieved in a 750-kHz bandwidth (about 800 kHz including guard bands). The information rate is calculated by dividing the 120 subchannels (tones) by the 200 xcexcs period to obtain 600 kbps.
For purposes of example for the present invention, xc2xd-rate convolutional codes (CC) are considered. The results with xc2xd-rate Reed-Solomon (RS) code based on Galois-Field (64) (GF(64)) are compared. The size of a code word is the same as that of an OFDM block (an OFDM symbol of 200 xcexcs and 120 subchannels). To achieve coding gain with inherent frequency diversity in OFDM, a simple interleaving scheme is applied. For both RS and CC cases, the first 120 bits of a code word are assigned to the in-phase component and the rest to the quadrature component. To gain additional randomness within a code word for the CC case, each 120-bit group is interleaved over subchannels by an 11-by-11 block interleaver (without the last bit).
In the simulations, the wireless channel, as a Rayleigh-fading channel, with a two-ray multipath delay profile is modeled. Good performance for impulse separation as high as 40-xcexcs can be achieved; a 5-xcexcs impulse separation in the numerical results is considered.
For the performance with respect to channel variations, maximum Doppler frequency up to 200 Hz, which is reasonable for most vehicular speeds, for a possible RF carrier frequency around 2 GHz is considered. To demonstrate the advantage of the proposed joint detection methods, results at a maximum Doppler frequency as high as 500 Hz corresponding to a scenario in which the wireless system uses a higher carrier frequency, e.g. 5 GHz are presented.
In the medium access control (MAC) layer, a frequency reuse is considered with dynamic resource management, e.g., Dynamic Packet Assignment (DPA), to achieve high spectral efficiency for packet data access.
A simple analysis to highlight the ideal or optimal joint channel estimation and maximum likelihood (ML) decoding scheme indicated in FIG. 1A for the case of M=2 receiving antennas is now presented.
At a diversity receiver, the signal from the m th antenna at the k th subchannel and the n th block can be expressed as
xm,n,k=hm,n,kan,k+wm,n,k, xe2x80x83xe2x80x83(1) 
where an,k, hm,n,k and wm,n,k are the transmit signal, channel response and additive Gaussian noise, respectively.
For convolutional codes, because the size of a code word is the same as that of the OFDM block, (1) can be rewritten as
xm,n=Hm,ncn+wm,n, xe2x80x83xe2x80x83(2) 
where, if there are Kf subchannels,
Hm,n=diag(hm,n,1, hm,n,2, . . . , hm,n,Kf), 
cn is the transmitted code word at time epoch n, and the rest of the vectors are similarly defined.
Assume that the number of code words is N, we introduce the following notations,
c=[c1T, c2T, . . . , cNT]T, 
Hm=diag(Hm,1, Hm,2, . . . , Hm,N), 
xm=[xm,1T, xm,2T, . . . , xm,NT]T. xe2x80x83xe2x80x83(3) 
At the receiver, the objective is to solve a maximum likelihood (ML) problem                                           c            ^                    =                                                    arg                ⁢                                  xe2x80x83                                ⁢                min                            c                        [                                          min                                  H                  m                                            ⁢                                                ∑                  m                                ⁢                                                      "LeftDoubleBracketingBar"                                                                  x                        M                                            -                                                                        H                          m                                                ⁢                        c                                                              "RightDoubleBracketingBar"                                    2                                                      ]                          ,                            (        4        )            
with a constraint on channel response
L(Hm)=0, xe2x80x83xe2x80x83(5) 
where L() is a constraint function. In a wireless environment, this constraint can be simplified to be                                                         ∑                              l                =                                  -                                      K                    m                                                                              K                m                                      ⁢                                          B                                  n                  ,                  l                                            ⁢                              d                ⁡                                  (                                      H                                          m                      ,                                              n                        -                        l                                                                              )                                                              =          0                ,                            (        6        )            
where the length of the channel memory is Km OFDM symbol durations, Bn,l are coefficients determined by the correlation between channel responses at the time epochs n and nxe2x88x921, which is a function of the Doppler spectrum of the channel, and d() is a vector function defined by
d(Hm,n)=[hm,n,1, hm,n,2, . . . , hm,n,Kf]T. 
The optimal solution of this ML problem can be obtained by exhaustive search. It requires solving the mean square error (MSE)                                           MSE            ⁡                          (              c              )                                =                                    min                              H                m                                      ⁢                                          ∑                m                            ⁢                                                "LeftDoubleBracketingBar"                                                            x                      m                                        -                                                                  H                        m                                            ⁢                      c                                                        "RightDoubleBracketingBar"                                2                                                    ,                            (        7        )            
for any possible c with the channel constraint (6). Then,                               c          ^                =                                            arg              ⁢                              xe2x80x83                            ⁢              min                        c                    ⁢                                    MSE              ⁡                              (                c                )                                      .                                              (        8        )            
After obtaining MSE(c), the corresponding channel estimate Hm(c) can be found. Consequently, the optimal approach for estimating channel response requires the knowledge of the entire set of x and c.
Another observation from this ML receiver is that the channel estimation results Hm is not a direct output of the detection process and hence, channel estimation which calculates Hm explicitly may not be necessary in theory. However, for other required parameter estimation, such as timing and frequency synchronization, a known data sequence is usually transmitted in the beginning of a group of OFDM blocks. This known data sequence, also called a synch word or a unique word, can be used as a training sequence in (7) to obtain initial channel estimate explicitly without resorting to blind detection. This initial channel characteristic is helpful for solving this ML problem with better numerical stability and tracking property. This initial channel estimation can be easily solved in the frequency domain by first taking FFT as shown in FIG. 1A.
One related method and system is Ser. No. 09/089,862, METHOD AND APPARATUS FOR CHANNEL ESTIMATION FOR MULTICARRIER SYSTEMS, which was filed Jun. 3, 1998, and is commonly held and incorporated herein by reference. The near optimal joint channel estimation and data detection method and system of the present invention was born from the research that resulted in that application and the subsequent determination that improvements could be made in the channel estimation.
The sub-optimal approach of the related system and method is now outlined. Because of the formidable complexity of the optimal ML receiver, some sub-optimal solutions are widely used in practice. The related sub-optimal solution is to divide the ML problem into two parts, channel estimation and coherent decoding. Then, the problem can be solved by iteratively estimating channel and decoding in the forward direction (in time).
At a time instant n, given a channel estimate Ĥm,n, initially obtained by using training sequence (in the frequency domain dividing the transfer function of the received signal by the transfer function of the known data), the maximum likelihood (ML) problem                                           c            ^                    n                =                                            arg              ⁢                              xe2x80x83                            ⁢              min                                      c              n                                ⁢                                    ∑              m                        ⁢                                          "LeftDoubleBracketingBar"                                                      x                                          m                      ,                      n                                                        -                                                                                    H                        ^                                                                    m                        ,                        n                                                              ⁢                                          c                      n                                                                      "RightDoubleBracketingBar"                            2                                                          (        9        )            
can be solved. Then, the reference for channel estimation is                                           H            ~                                m            ,            n                          =                                            arg              ⁢                              xe2x80x83                            ⁢              min                                      H                              m                ,                n                                              ⁢                                    ∑              m                        ⁢                                                            "LeftDoubleBracketingBar"                                                            x                                              m                        ,                        n                                                              -                                                                  H                                                  m                          ,                          n                                                                    ⁢                                                                        c                          ^                                                n                                                                              "RightDoubleBracketingBar"                                2                            .                                                          (        10        )            
Finally, the estimate for the time instant n+1 is obtained by solving a linear constrained equation (6). Considering a stationary channel with fixed maximum Doppler frequency, the coefficients Bn,l are independent of n, and can be written as Bl, which are used as the coefficients in the FIR filter to track channel variations. Consequently, a simplification of (6) with only previous references for prediction-type estimation leads to                                                                         ∑                                  l                  =                  1                                                  M                  L                                            ⁢                                                B                  l                                ⁢                                  d                  ⁡                                      (                                                                  H                        ~                                                                    m                        ,                                                  n                          +                          1                          -                          l                                                                                      )                                                                        -                          d              ⁡                              (                                                      H                    ^                                                        m                    ,                                          n                      +                      1                                                                      )                                              =          0                ,                            (        11        )            
where Ml is the number of taps of an FIR filter and Bl are preset coefficients designed to achieve the minimum mean square error (MMSE) of estimation. This MMSE estimator can be realized by a frequency-domain filter using the Fast Fourier Transform (FFT), followed by an Ml-tap time-domain filter,
Bl=blFxe2x88x921BfF, xe2x80x83xe2x80x83(12) 
where bl is the time-domain filter coefficient, F is the FFT matrix, Bf is a diagonal matrix, and Fxe2x88x921BfF is the frequency-domain filter.
The MMSE filter coefficients bl and Bf were derived assuming ĉn=cn for a given set of Doppler frequency and delay spread. It is shown that this estimator is robust regardless of frequency or time mismatches. With a low Doppler frequency, it has been shown, that a 5-tap (Ml=5) estimator can successfully predict the channel.
To obtain accurate initial channel estimation, a training OFDM block is sent at the beginning of a transmission, in which c1 is known to obtain {tilde over (H)}m,1. The channel parameters for the new time epochs and the unknown code words can be successively solved in the forward direction (time advance).
The assumption ĉn=cn cannot be always guaranteed; an incorrectly detected code word introduces wrong channel estimation and hence, can cause a wrong detection of the successive code words. This error propagation is the dominant impairment of the link performance at high SNR. In order to alleviate the problem of error propagation, a training OFDM block is inserted every Nt block. In the simulations presented herein, Nt=10 is considered.
In FIG. 2, the performance of the coherent reception with RS code and convolutional codes for 40-Hz maximum Doppler frequency is shown. The convolutional codes are shown with different constraint length (K) ranging from 3 to 9 as dashed lines. The performance of convolutional codes is substantially better than that of the RS code, which is shown as a solid line with cross lines. In order to achieve a Word Error Rate (WER) of 10xe2x88x922, the K=9 CC needs 4 dB lower SNR than the RS code. In the use of WER in the present invention, it is assumed that a word is a codeword. Moreover, the performance of the K=9 CC with channel estimation is very close to the one with the ideal channel information shown as a solid line.
In FIG. 3, the performance at 200-Hz Doppler is shown. In comparison with the RS code, the CC""s are still superior although the degradation with respect to the idealized case is higher due to poorer channel tracking. In fact, an error floor at the high SNR region exists due to tracking errors. Once again the RS coded signal is indicated as a solid line with cross lines. The convolutionally coded signals are indicated by dashed lines and ideal channel information is indicated by a solid line.
In FIG. 4, the performance of the K=9 CC with different maximum Doppler frequencies is shown. With a low Doppler frequency, a 5-tap (Ml=5) estimator used here can successfully predict the channel and the performance is very close to that with idealized channel estimation. However, when the fading is relatively fast, it is difficult to estimate the channel correctly and the WER floors on the order of 10xe2x88x923 can be clearly observed for at a maximum Doppler frequency of 200 Hz. That is, it was found that the original method works well in slow fading but degrades significantly in fast fading. Once again the ideal Doppler frequency is indicated by a solid line. A Doppler frequency of 200 Hz is indicated by a dashed line. A Doppler frequency of 175 Hz is indicated by a dashed line with small circles. A Doppler frequency of 150 Hz is indicated by a dashed line with triangles and a Doppler frequency of 125 Hz is indicated by a dashed line with cross lines.
FIG. 1B depicts a block diagram for a baseband receiver. It is simplified to the extent that only channel estimator and decoder portions of the receiver are depicted. The decoder further comprises a plurality of demodulators, as well as a maximum ratio combiner, an optional deinterleaver (to match an optional interleaver in the transmitter) and a Viterbi decoder, all depicted in FIG. 1A. However, FIG. 1B depicts the structure and corresponding connections of the receiver depicted in FIG. 1A. Note, all x, ĉ, Ĥ, {tilde over (H)} are complex. Although it may seem strange to have a complex codeword, ĉ, it is very natural to treat coding and modulation as a whole like spatial-temporal coding as discussed in xe2x80x9cSpace-time codes for high data rate wireless communication: performance criterion and code constructionxe2x80x9d, by V. Tarokh, N. Seshadri, and A. Calderbank, published in IEEE Trans. Info. Theory, vol. 44, no. 2, pp. 744-765, March 1998 or coded modulation xe2x80x9cChannel coding with multilevel/phase signals,xe2x80x9d by G. Ungerboeck, published in IEEE Trans. Info. Theory, vol. IT-28, no. 1, pp. 55-67, January 1982.
At a time instant n, the channel estimator unit has two tasks. One is to produce the channel estimates of current time instant, Ĥ1,n, Ĥ2,n, . . . with its input x1,n, x2,n, . . . and feedback {tilde over (H)}1,,nxe2x88x92Ml, {tilde over (H)}2,nxe2x88x92Ml, . . . , {tilde over (H)}l,nxe2x88x921, {tilde over (H)}2,nxe2x88x921,, by equation (11). The other task is to produce references {tilde over (H)}1,n, {tilde over (H)}2,n, . . . for estimate processing in the next time instant by equation (10) when ĉn is available. At a time instant n, when Ĥ1,n, Ĥ2,n, . . . are available, the decoder unit produces decoded information ĉn by (9).
The flowchart of this method is shown in FIG. 1c. The related channel estimation method is first initialized at step 165-1. Transmitted signals are received at step 165-2. A determination is then made at step 165-3 as to whether the received block is a training block. If the received block is a training block then ĉn is known and             H      ~              m      ,      n        =                    arg        ⁢                  xe2x80x83                ⁢        min                    H                  m          ,          n                      ⁢                  ∑        m            ⁢                        "LeftDoubleBracketingBar"                                    x                              m                ,                n                                      -                                          H                                  m                  ,                  n                                            ⁢                                                c                  ^                                n                                              "RightDoubleBracketingBar"                2            
is calculated at step 165-5. This is a reference for the channel estimation                     ∑                  l          =          1                          M          L                    ⁢                        B          l                ⁢                  d          ⁢                      (                                          H                ~                                            m                ,                                  n                  +                  1                  -                  l                                                      )                                -          d      ⁢              (                              H            ^                                m            ,                          n              +              1                                      )              =  0
which is calculated next at step 165-6. The block number is incremented at step 165-7 and a determination is made if the end of the frame has been reached at step 165-8. If the current block is not a training block then ĉn is decoded at step 165-4             c      ^        n    =                    arg        ⁢                  xe2x80x83                ⁢        min                    c        n              ⁢                  ∑        m            ⁢                        "LeftDoubleBracketingBar"                                    x                              m                ,                n                                      -                                                            H                  ^                                                  m                  ,                  n                                            ⁢                              c                n                                              "RightDoubleBracketingBar"                2            
is calculated before calculating the reference and channel estimation.
It should be clear from the foregoing that there is room for improvement between the prior art and optimal joint channel estimation and data detection. An object, therefore, of the present invention is to improve the joint channel estimation. This will have the effect of reducing the impact of noise as well as reducing decoding errors. Thus, overall system performance will be improved.
It is a further object of the present invention to provide a method and system that are robust even in light of a mismatch between Finite Impulse Response (FIR) coefficients and the true channel.
Another object of the present invention is to provide a method and system with improved channel tracking capability, resulting in reliable link performance even under high user mobility and/or high RF carrier frequency. With improved link performance, data rates significantly higher than currently available (or even than third generation systems in planning) can be offered to subscribers.
All of the above objects can be achieved nearly optimally even in rapid dispersive fading channels.